Scotland’s National Clinical Director said that even though this was only around 10% to 15% of the population, it was still a “significant number of people”.
Appearing on the BBC’s Good Morning Scotland radio programme on Tuesday, Prof Leitch was also asked about the situations in East Renfrewshire and Midlothian, where cases are rising.
Glasgow and Moray remain in Level 3 restrictions despite the rest of mainland Scotland moving to Level 2 on Monday.
Discussing the vaccination efforts in Glasgow, Prof Leitch said: “The ones most likely to get seriously unwell are the percentage difference between 100 and those we managed to vaccinate in that older age group.
“It’s somewhere between 10-15%. In some places it’s only 5%.
“But 5% of a big number is a big number. So it’s still a significant number of people that we really want to get vaccinated.”
He urged people who had missed either a first or second dose to come forward, saying “we’d love to give you that full protection”.
Public health teams in Glasgow have also decided to offer vaccination to some in the 18 to 39-year-old age group.
Prof Leitch said there had been a “little uptick” of cases in Midlothian and East Renfrewshire, saying the First Minister and her new cabinet would take a decision later this week on whether levels of restriction needed to change.
The national clinical director also responded to comments from Professor Sir John Curtice, who said he had struggled with the Scottish Government’s vaccine helpline.
Sir John, 67, told The Herald that he had waited more than 14 weeks for his second dose and the helpline team had been unable to resolve the issue despite three weeks of calls.
Prof Leitch said he was “sorry” Sir John had gone through three weeks of consultation without success, but there was “no difference clinically” between a 12-week and 14-week wait.
He said: “I don’t think it’s fair to say the helpline is not working.
“I think it’s fair to say there are some people for who the helpline isn’t working as quickly as it should and we’re trying to correct that as much as we can.”